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Paper Citation Record · LEDGER

Thermodynamics and Legendre Duality in Optimal Networks

As of 13 August 2026, this Paper Citation Record lists 80 of 80 outbound references and 0 inbound Pith citation observations for arXiv:2506.15727.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2506.15727 v1

Coverage vector

measured 80 of 80 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:33:21.307241Z

measured 80 of 80 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

80 of 80 outbound references displayed

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  • verified fuzzy52
  • unresolved28
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  • malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a065bdeb-a4cb-42e5-a077-23870794e641 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 1

Resolution
unresolved
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 66e714a7-4c9d-49b1-b0a0-329161b843af · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 2

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 2441017f-bb57-4ace-a239-814b219070fc · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 3

Resolution
unresolved
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation ddfbf355-55c3-4eef-a2b5-ea234c37319c · outbound

This paper cites Rodriguez-Iturbe, A.

Thermodynamics and Legendre Duality in Optimal Networks Rodriguez-Iturbe, A

Reference 4

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation f185aea9-b652-4813-8816-d45dfaab8b1d · outbound

This paper cites Santambrogio, Optimal transport for applied mathematicians, Birk¨ auser, NY 55 (58-63) (2015) 94.

Thermodynamics and Legendre Duality in Optimal Networks Santambrogio, Optimal transport for applied mathematicians, Birk¨ auser, NY 55 (58-63) (2015) 94

Reference 5

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 871c065b-6baa-430c-b3ae-c3072f4bc94b · outbound

This paper cites Van Baak, Variational alternatives to kirchhoff’s loop theorem in dc circuits, American Journal of Physics 67 (1) (1999) 36–44.

Thermodynamics and Legendre Duality in Optimal Networks Van Baak, Variational alternatives to kirchhoff’s loop theorem in dc circuits, American Journal of Physics 67 (1) (1999) 36–44

Reference 6

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation e2d67628-56a3-4d73-8a53-15d61916df8c · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 7

Resolution
unresolved
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:20.963790Z digest=sha256:cedf8a00a3b3b6ded2ac14a51fd2dd1ea7b89aaab604343cfac340c502eb0b56

Observation 07941dc3-f4a7-49da-910a-176a34d88b5b · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:32.932284Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:20.968823Z digest=sha256:978a1f8b512bd2263a253b0b0238a1a3e124492b3f9dab0236105f232a739290

Observation cc9e931d-dd99-4379-85ec-07371df9640f · outbound

This paper cites Barbera, On the principle of minimal entropy production for navier-stokes-fourier fluids, Continuum Mechanics and Thermodynamics 11 (5) (1999) 327–330.

Thermodynamics and Legendre Duality in Optimal Networks Barbera, On the principle of minimal entropy production for navier-stokes-fourier fluids, Continuum Mechanics and Thermodynamics 11 (5) (1999) 327–330

Reference 9

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 96a13060-834e-4998-a5a0-afa7543327e3 · outbound

This paper cites Kondepudi, I.

Thermodynamics and Legendre Duality in Optimal Networks Kondepudi, I

Reference 10

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 8a6e7795-190b-4059-b45b-6f5e4a08f339 · outbound

This paper cites Martyushev, A.

Thermodynamics and Legendre Duality in Optimal Networks Martyushev, A

Reference 11

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 4856ca3f-f057-422e-8505-6312cde9e12e · outbound

This paper cites Millar, Cxvi.

Thermodynamics and Legendre Duality in Optimal Networks Millar, Cxvi

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:32.274682Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:20.988944Z digest=sha256:3b8d828ea19bd092685ea645c8480740320be2e6b90855264a9aa16ccaf75087

Observation f169b4f6-f3e6-4c86-b9b3-d3521fa351bd · outbound

This paper cites Cherry, Non-linear circuit theory by the methods of classical dynamics, in: Recent Developments in Network Theory, Elsevier, 1963, pp.

Thermodynamics and Legendre Duality in Optimal Networks Cherry, Non-linear circuit theory by the methods of classical dynamics, in: Recent Developments in Network Theory, Elsevier, 1963, pp

Reference 13

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 6dcb97e7-6e10-4e72-ad49-22e328c03e74 · outbound

This paper cites Verh´ as, Gyarmati’s variational principle of dissipative processes, Entropy 16 (4) (2014) 2362–2383.

Thermodynamics and Legendre Duality in Optimal Networks Verh´ as, Gyarmati’s variational principle of dissipative processes, Entropy 16 (4) (2014) 2362–2383

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:31.887390Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 98ee0a3b-686c-4cfc-9845-d8e1780c45e7 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 15

Resolution
unresolved
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation fa2828a4-92a0-4eac-ae42-492af6e3e2a0 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 16

Resolution
unresolved
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 37106f81-5467-4fc3-89ff-666da53c3f64 · outbound

This paper cites Bejan, S.

Thermodynamics and Legendre Duality in Optimal Networks Bejan, S

Reference 17

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 0d5c1ce7-94ec-498f-98e8-3386b5713e80 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:31.049138Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 9e33c85d-b658-4372-9e29-212cb42c6ba9 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:30.836691Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation af34757c-bef0-4203-8e21-81491eaf5ba0 · outbound

This paper cites Rinaldo, R.

Thermodynamics and Legendre Duality in Optimal Networks Rinaldo, R

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:30.607866Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 57a38811-0b57-4f5b-a6dd-d50992981e4d · outbound

This paper cites Bandle, Dido’s problem and its impact on modern mathematics, Notices of the AMS 64 (9).

Thermodynamics and Legendre Duality in Optimal Networks Bandle, Dido’s problem and its impact on modern mathematics, Notices of the AMS 64 (9)

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:30.470890Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 98efe4aa-1045-4b98-91d5-fd484cf7b39a · outbound

This paper cites Hooshyar, S.

Thermodynamics and Legendre Duality in Optimal Networks Hooshyar, S

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:30.345312Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 269f0bb4-7408-460c-95bb-de1b34335bf5 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 23

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:30.132449Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 49cff04c-5d14-4839-b166-8319817d2265 · outbound

This paper cites Facca, F.

Thermodynamics and Legendre Duality in Optimal Networks Facca, F

Reference 24

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation fc119b5e-981d-4eb0-9510-2bde90366e80 · outbound

This paper cites Mrugala, J.

Thermodynamics and Legendre Duality in Optimal Networks Mrugala, J

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:29.792301Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 8517ec12-a603-4b54-8887-88187dbe596f · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 26

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:29.491703Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 806a7299-caef-4a65-a90f-52c723fc93b3 · outbound

This paper cites Schnakenberg, Network theory of microscopic and macroscopic behavior of master equation systems, Reviews of Modern physics 48 (4) (1976) 571.

Thermodynamics and Legendre Duality in Optimal Networks Schnakenberg, Network theory of microscopic and macroscopic behavior of master equation systems, Reviews of Modern physics 48 (4) (1976) 571

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:29.262278Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation a72f3a37-5a94-4a64-9003-eb7bdad4149d · outbound

This paper cites Oster, C.

Thermodynamics and Legendre Duality in Optimal Networks Oster, C

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:29.090999Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation f3084f35-4a8f-4c52-a0e1-e97adb0823d5 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 29

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:28.913765Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.070815Z digest=sha256:ec24026c1287d1a787b941ce94a023fedb1533a5ea05e68be2f4f4238fd18f42

Observation 08d11f20-9f43-4da1-ad9c-763c12919750 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 30

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:28.706338Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 48cad465-364e-42a5-bd8f-52e3049dd0ad · outbound

This paper cites Onsager, S.

Thermodynamics and Legendre Duality in Optimal Networks Onsager, S

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:28.518735Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation 3ceafdb9-7fc5-42e0-abc3-61ed0ebf4862 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 32

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:28.297224Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.084827Z digest=sha256:593cedc474929f5fe0ce340948bfca250b1ca6da94803e8964a7b52d2ccdf1bf

Observation 64b60d3a-6a2b-459e-8650-241000e97c65 · outbound

This paper cites Doi, Onsager’s variational principle in soft matter, Journal of Physics: Condensed Matter 23 (28) (2011) 284118.

Thermodynamics and Legendre Duality in Optimal Networks Doi, Onsager’s variational principle in soft matter, Journal of Physics: Condensed Matter 23 (28) (2011) 284118

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:28.121574Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation b0228743-28d2-4a5c-ac04-e844e9eb46df · outbound

This paper cites Bataille, D.

Thermodynamics and Legendre Duality in Optimal Networks Bataille, D

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:27.931097Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

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Observation b96c3a07-64ff-4cbd-95d2-1651b8c8f74e · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 35

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:27.723856Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.099469Z digest=sha256:dfac881233646f13e57937c8c7eec209f49d2b991f331a84c49cbf7b009a1b7d

Observation 5a0f92d8-7522-4992-a3a4-290b03c4520d · outbound

This paper cites Sewell, Complementary energy and catastrophes, in: Variational Methods in the Mechanics of Solids, Elsevier, 1980, pp.

Thermodynamics and Legendre Duality in Optimal Networks Sewell, Complementary energy and catastrophes, in: Variational Methods in the Mechanics of Solids, Elsevier, 1980, pp

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:27.509220Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.103871Z digest=sha256:2af0f7dc7139a935ee58697902af48930e6d283d877da23b42c30b49f82645c0

Observation c4bbc2ef-27f9-456d-a683-910328fc2600 · outbound

This paper cites Gyarmati, et al., Non-equilibrium thermodynamics, Vol.

Thermodynamics and Legendre Duality in Optimal Networks Gyarmati, et al., Non-equilibrium thermodynamics, Vol

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:27.301920Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.108691Z digest=sha256:a74ac066953e13ce3fd8437678585d2f8d930f29b3aeff984f82a41dca64e5f5

Observation 0e017a57-89bd-469d-9aee-15b8344475fc · outbound

This paper cites Biolek, D.

Thermodynamics and Legendre Duality in Optimal Networks Biolek, D

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:27.082729Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.113035Z digest=sha256:506ada0c2bc5c565cd5cc7ca824cc1e93f5dc8e5f56c1368525a6450fe1be6cd

Observation e4078341-e11c-4077-82b9-82fff929b02a · outbound

This paper cites Ziegler, An introduction to thermomechanics, Elsevier, 2012.

Thermodynamics and Legendre Duality in Optimal Networks Ziegler, An introduction to thermomechanics, Elsevier, 2012

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:26.900967Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.117427Z digest=sha256:3093c06577e72cba46a167d635114a6a6a864f1437c0f78cc4becdda488d1e1c

Observation 7c85d655-e8a5-403b-9cc3-c2ca9a73fa29 · outbound

This paper cites Gallavotti, Statistical mechanics: A short treatise, Springer Science & Business Media, 2013.

Thermodynamics and Legendre Duality in Optimal Networks Gallavotti, Statistical mechanics: A short treatise, Springer Science & Business Media, 2013

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:26.708417Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.121810Z digest=sha256:7e6f9caf7d10397f0f6472e2f5de4d1339fd84c801b90faf0972a1e61997f46d

Observation 430b49dc-171b-4840-b91a-6054721dc72e · outbound

This paper cites ˇZupanovi´ c, D.

Thermodynamics and Legendre Duality in Optimal Networks ˇZupanovi´ c, D

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:26.459542Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.126049Z digest=sha256:18c1b6d797de1fb39c05c079dee6e73d30670ed0e2cf41e4270c873248d3ad6e

Observation 56e76cdd-8d5e-4091-8f5d-234b5bb3b954 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 42

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:26.204696Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.130308Z digest=sha256:bdb0a0d3808955227c43abb2906f16adcd1248412b5956be79754ee02bab48f4

Observation 8a14c1b8-a2f9-4fca-acdd-1b21703d49fd · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 43

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:25.979268Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.135222Z digest=sha256:aa580ea6aa8b78ab0f60650b87e02cd326c0fb8c6f2151629387ddb5cca0970a

Observation fd6e830b-285a-4d15-88eb-7de1eef2b467 · outbound

This paper cites Porporato, S.

Thermodynamics and Legendre Duality in Optimal Networks Porporato, S

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:25.781269Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.140079Z digest=sha256:cec6b2ff01be99e71e8dc626a5f81861690310b4c88ca83f0cba3e7bcded2d92

Observation 30299500-509f-4caf-aa22-91ce3512e3bc · outbound

This paper cites Schl¨ ogl, Thermodynamic metric and stochastic measures, Zeitschrift f¨ ur Physik B Condensed Matter 59 (4) (1985) 449–454.

Thermodynamics and Legendre Duality in Optimal Networks Schl¨ ogl, Thermodynamic metric and stochastic measures, Zeitschrift f¨ ur Physik B Condensed Matter 59 (4) (1985) 449–454

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:25.588584Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.144813Z digest=sha256:a0946656c7c896c9d973842037fe0447f7595e09d42c0a77802f1cde3b71520f

Observation b06a446c-fdd5-42b1-add3-1895bbe63e6a · outbound

This paper cites Mrugala, J.

Thermodynamics and Legendre Duality in Optimal Networks Mrugala, J

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:25.336653Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.149261Z digest=sha256:c65eaf5396233caf21fdaffa94b94c01965baedd376375b71f3e9a3f1a2e2cc9

Observation 092520c9-0ca6-4cce-a728-1f0a214821cb · outbound

This paper cites Brody, N.

Thermodynamics and Legendre Duality in Optimal Networks Brody, N

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:25.110479Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.154078Z digest=sha256:4e5fab218d7c7129770157b4dc9e99057bab12de1dfa3cc894c9bbc51c76d030

Observation 7590a5c9-3d7c-44d2-ba8d-8947d98b2944 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 48

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:24.879402Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.158804Z digest=sha256:0531c453d9d3608a8b61da9c6590761c385f6e6ce78f145932d1034cc8a63416

Observation b9074e50-eb92-4f5b-9f5c-32c0ac788904 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 49

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:24.760150Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.163390Z digest=sha256:2727f4896da85b09fd4fa2f33075ca1886de326d0e97ede24aae1760f4355665

Observation 22e66c23-6678-4062-a0e8-4b8725b11eb3 · outbound

This paper cites Ercan, On kirchhoff’s equations and variational approaches to electrical network analysis, American Journal of Physics 84 (3) (2016) 231–233.

Thermodynamics and Legendre Duality in Optimal Networks Ercan, On kirchhoff’s equations and variational approaches to electrical network analysis, American Journal of Physics 84 (3) (2016) 231–233

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:24.592563Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.167842Z digest=sha256:3f0d023ec57cc4ba956ede3ce466677fe5ac72ebfe6eaa5a26569b27435ab122

Observation 75d696d1-abe1-420d-b1bb-3b4fb409ee1b · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 51

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:24.417598Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.172481Z digest=sha256:ff529c9debfda1564917e82ff5095a0befdc68c7670fb7eaa600299f3c59de74

Observation 5350e943-4ae1-4917-bc0d-e9f0dbec3098 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 52

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:24.254134Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.176876Z digest=sha256:51ddc02e55d54bac7d772514597e6b687f34618d0e12c83a3c0cdf11138312c3

Observation e90ecb08-25e2-44fd-9d1c-ef98f5c51b27 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 53

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:24.054150Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.181606Z digest=sha256:245a3b6f690cb470fabd2e48d3ec51aca37bec569da6d59e819104cba538db84

Observation 9d4b41be-2d01-4f95-81a8-ffb2c56b3b7f · outbound

This paper cites Kawazura, Z.

Thermodynamics and Legendre Duality in Optimal Networks Kawazura, Z

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:23.892350Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.185987Z digest=sha256:50894230d9f1ecfa09a1cc665fd8b809eefbc38d4961f19c48ab6ed1bd8e750e

Observation 0d25b65e-077f-4e0e-a033-6828adb2e852 · outbound

This paper cites Martyushev, Some interesting consequences of the maximum entropy production principle, Journal of Experimental and Theoretical Physics 104 (2007) 651–654.

Thermodynamics and Legendre Duality in Optimal Networks Martyushev, Some interesting consequences of the maximum entropy production principle, Journal of Experimental and Theoretical Physics 104 (2007) 651–654

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:23.642601Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.190487Z digest=sha256:601d98a3ed8ce39a4f59180ac7681658fe4272a997acb1a7e2d25e856453ef7f

Observation 4f8a2d9a-fbfd-4b77-a843-c3631bb48c72 · outbound

This paper cites Hill, Entropy production as the selection rule between different growth morphologies, Nature 348 (1990) 426–428.

Thermodynamics and Legendre Duality in Optimal Networks Hill, Entropy production as the selection rule between different growth morphologies, Nature 348 (1990) 426–428

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:23.358734Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.195131Z digest=sha256:370ce379995bb3f0184ac04b65c7a0656fe10df4e47e69b11c70cd27951aa078

Observation e76c3b84-6bb4-4186-8ce8-4c93ff9cc540 · outbound

This paper cites Ozawa, S.

Thermodynamics and Legendre Duality in Optimal Networks Ozawa, S

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:23.142761Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.199386Z digest=sha256:85f40621aa6b055962b707457a0377f0246d3b1f57d7f920f79cacf4947be1ae

Observation 194763ac-27ff-4c24-ac0d-04e81a939ec3 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 58

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:22.918614Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.204078Z digest=sha256:01b4ad435c2a008a161e3680d2835739fd43da73ae540c2f05d8a0d6a597b192

Observation 0b04e7e7-d5ea-48fb-a05e-e839e3a6067f · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 59

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:22.758594Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.208743Z digest=sha256:b05e10db1b51dfd7745d2b875d1e1f490ff7110f09e4f98bcc692d296c910607

Observation d0d156cc-d1eb-4519-9fc4-c98fca579516 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 60

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:22.553892Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.213392Z digest=sha256:8cad6f3dd83f2e36d06186bcd771098fef89d13798efa370c0f5b4d35b387bc0

Observation e19a255b-ab4e-40c6-86d0-92f34b4dd316 · outbound

This paper cites Yoshida, S.

Thermodynamics and Legendre Duality in Optimal Networks Yoshida, S

Reference 61

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:22.392772Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.218367Z digest=sha256:29fe015c91c4f96f91670427ad2b9ad6ff7166ecc373b410002729490ebd6f01

Observation f8fa01c8-198a-4c3b-9c02-e6b19737102f · outbound

This paper cites Yoshida, Y.

Thermodynamics and Legendre Duality in Optimal Networks Yoshida, Y

Reference 62

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:22.218248Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.223616Z digest=sha256:78374a1d9aaa50ced701d9d92b0a2ea18f1f8f94d746edec92b3dd978265a2db

Observation a57dc63a-43e2-45e1-ba77-b4158bcb0ce1 · outbound

This paper cites Kawazura, Z.

Thermodynamics and Legendre Duality in Optimal Networks Kawazura, Z

Reference 63

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:22.105747Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.228557Z digest=sha256:06fa7919ec6231fe8f19b38f3790e8b016762b8050efbd6735783834b2d7408f

Observation 1f91d8a3-f994-47b6-9fd1-7aa647d2a717 · outbound

This paper cites Glansdorff, I.

Thermodynamics and Legendre Duality in Optimal Networks Glansdorff, I

Reference 64

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:21.982485Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.233777Z digest=sha256:27e45dcb9b6da5e6f9a3416bdad5b0551cd3ca5593b701d473507ef8dbfe50fa

Observation f69d556d-9383-4d1d-b98b-b097c46546a1 · outbound

This paper cites Landauer, Stability and entropy production in electrical circuits, Journal of Statistical Physics 13 (1975) 1–16.

Thermodynamics and Legendre Duality in Optimal Networks Landauer, Stability and entropy production in electrical circuits, Journal of Statistical Physics 13 (1975) 1–16

Reference 65

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:21.845645Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.238383Z digest=sha256:fa08820bb5ff8c38bd419e333d012a17f482ba2707a9a19ba43e996a33a33b6a

Observation 6385e238-4510-422c-800d-4474f07b6aa4 · outbound

This paper cites Bodineau, B.

Thermodynamics and Legendre Duality in Optimal Networks Bodineau, B

Reference 66

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:21.740057Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.242842Z digest=sha256:ee36ab9434855a5e11e1f5fbdcfec36c526db41dd7b817d43daf3ed293b62c81

Observation 7ec3b028-4229-4bf6-a242-db0e702724ca · outbound

This paper cites Derrida, J.

Thermodynamics and Legendre Duality in Optimal Networks Derrida, J

Reference 67

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:21.676082Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.247409Z digest=sha256:8680214d8981748b73054ff56206cf8ad2f080a81ebd55ade5f6afe4843fca15

Observation 2caff210-ba5e-4e17-b44c-6fd61ebcbb73 · outbound

This paper cites Bertini, A.

Thermodynamics and Legendre Duality in Optimal Networks Bertini, A

Reference 68

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:21.615529Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.251904Z digest=sha256:072aaeeaf287cafbdcac3f48a9c17be378165dc4383af2bc234851d3e570d51f

Observation 68ec7cd6-0360-4b24-bd4a-b61eb5c71e31 · outbound

This paper cites Torquato, Optimal design of heterogeneous materials, Annual review of materials research 40 (1) (2010) 101–129.

Thermodynamics and Legendre Duality in Optimal Networks Torquato, Optimal design of heterogeneous materials, Annual review of materials research 40 (1) (2010) 101–129

Reference 69

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:21.580139Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.256917Z digest=sha256:d80b75ed44a3300633a91270d04c0ecd270856ac872fbe0f0192c45831b06f9c

Observation 574d4ea4-09b1-42c3-92a3-257bfbf7ead4 · outbound

This paper cites Waldherr, D.

Thermodynamics and Legendre Duality in Optimal Networks Waldherr, D

Reference 70

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:21.557838Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.261139Z digest=sha256:44efe65d4d4bcc0acba2670ddabb223f12bd31358f21c7a8b349d52332e3bbb3

Observation 988a15a6-96e3-499b-bb44-50210b31ccff · outbound

This paper cites Franklin, S.

Thermodynamics and Legendre Duality in Optimal Networks Franklin, S

Reference 71

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:21.533585Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.265258Z digest=sha256:76dc5a4fbc859e7fb3acbaa0bd9e21aa57167c14a6e236e4fb70633c2ca93f45

Observation 973005cd-66be-4c31-95b3-7cac2cbfbf12 · outbound

This paper cites Calabrese, B.

Thermodynamics and Legendre Duality in Optimal Networks Calabrese, B

Reference 72

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:21.507547Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.269652Z digest=sha256:53cee2b8876c08e420d53459bcdba847834f5baa2b3eb838fb42ccd2c590a2dd

Observation 26caf9fe-689f-475d-936f-54dff3aff9ce · outbound

This paper cites Witelski, M.

Thermodynamics and Legendre Duality in Optimal Networks Witelski, M

Reference 73

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:21.481941Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.274297Z digest=sha256:17ccf7c8e15e547da5a9fe5adcef0bc021ba051322ec73d2f1e14584a1ac8269

Observation 7550b0c6-3660-47ab-93da-84cb728d5346 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 74

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:21.460848Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.278618Z digest=sha256:c30d3b14085f94949f1cc2717a6157dc67b2961d298673f0c49bada204461b6e

Observation f366eb38-1e2a-4965-9342-6de5ed467b35 · outbound

This paper cites Giaccone, S.

Thermodynamics and Legendre Duality in Optimal Networks Giaccone, S

Reference 75

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:21.435638Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.283029Z digest=sha256:e58346574fba36649855b4327e018d9c429a46023a4681bb2b96d098a4e96ee5

Observation 73b80792-d2a1-48af-b70f-70e962a15f23 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 76

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:21.414149Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.287674Z digest=sha256:774b0978e3fb40a41b2ba835feb60015413807d30396dd4a041fe9e386e147ae

Observation 25bc5904-daa7-42ff-b4be-50250aa95aa1 · outbound

This paper cites Burger, J.

Thermodynamics and Legendre Duality in Optimal Networks Burger, J

Reference 77

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:21.394832Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.292634Z digest=sha256:f04b9519b19caa60cf7569fad16746f5046d69def013c30ec4b17e95300e8302

Observation 68c65f00-4840-460c-9726-0e8fb01527f6 · outbound

This paper cites an unresolved cited work.

Thermodynamics and Legendre Duality in Optimal Networks Unresolved cited work

Reference 78

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:33:21.379227Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.297764Z digest=sha256:3898b603e93a042710a604f2622efca11e5ad123fa46d6b341c3342942e6ab22

Observation 9f4750d6-7403-4824-b1f2-fa4163915783 · outbound

This paper cites Bonetti, M.

Thermodynamics and Legendre Duality in Optimal Networks Bonetti, M

Reference 79

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:21.362961Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.302767Z digest=sha256:7c96877b5d3f8dc635773bc661a45105dc339602f69a8a80f70e2ad7331ecf6c

Observation 104fbc02-6dab-41a2-b8ca-e95f914c2665 · outbound

This paper cites Maritan, F.

Thermodynamics and Legendre Duality in Optimal Networks Maritan, F

Reference 80

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:33:21.346917Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-07T05:33:21.307241Z digest=sha256:c440f7beb22927c6cc7d5453856cb82021982d5c7ee6028654b4a3af4e977dea

Pith citing papers

No inbound Pith citation observations are available.